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**Proving Angle Relationships**

Chapter 2 Section 8

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**Angle Addition Postulate**

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**Using the Angle Addition Postulate**

1 EXAMPLE Using the Angle Addition Postulate 75

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**Find the measure of each numbered angle and name the theorem that justifies your work.**

They are a linear pair, so they will add to 180. Solve for x. All angles add to 180. Solve for x. Angles 1 and 2 add to 90. Angles 11 and 13 add to 180.

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**Properties of Congruent Angles**

Reflexive Property ∠ A ≅ ∠ A Symmetric Property If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A Transitive Property If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C

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**Theorem 2.4:Congruent Supplements Theorem**

If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.

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**Theorem 2.5:Congruent Complements Theorem**

If two angles are complementary to the same angle (or to congruent angles), then they are congruent.

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**Theorem 2.8 Vertical Angles Theorem**

Vertical angles are congruent. 2 3 1 4 ∠1 ≅ ∠3; ∠2 ≅ ∠4

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**Example – Using Vertical Angles Theorem**

Find the value of x 4x 3x + 35 What is each angle measure? Set 4x = 3x + 35 Solve for x

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Right Angle Theorems

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**More right angle theorems**

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Have a great day!

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